IndisputableMonolith.Physics.CouplingLockIn
This module defines the lock-in scale Q_lock as the fundamental recognition scale Q_lock = hbar / ell0 together with predicates for locked coupling regimes. It supplies the scale at which running couplings from the phi-ladder stabilize, for use in RG analyses anchored at the RS recognition point. The module consists entirely of definitions with no proofs.
claimThe lock-in scale is the recognition scale $Q_ {lock} = hbar / ell_0$. It induces the locked regime predicate $alpha_locked$ and the scale-dependent lock $alpha_lock_at_scale(mu)$, together with the continuous inverse $alpha_inv_phys_continuous$ and the regime indicator $is_locked_regime$.
background
Recognition Science anchors all couplings at the recognition scale via the phi-ladder. The upstream Constants module supplies the RS time quantum tau_0 = 1 tick. The upstream RunningCouplings module establishes the RG flow with stationary point mu* = 182.201 GeV, beta-function structure beta(g) = (1/ln phi) dg/dr, and the sign of asymptotic freedom fixed by the SU(3) color structure from Q_3. This module introduces the lock-in scale Q_lock = hbar / ell0 as the point where these flows stabilize.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the lock-in definitions that anchor the alpha band (137.030 to 137.039) and feed the beta-function derivations in RunningCouplings. It realizes the stationarity condition at the recognition scale required by the phi-ladder derivative in the RG flow, connecting directly to the T5 J-uniqueness and T6 phi fixed-point steps of the forcing chain.
scope and limits
- Does not derive ell0 from the forcing chain.
- Does not compute numerical values of alpha_locked.
- Does not include higher-loop corrections to the beta function.
- Does not address non-perturbative effects beyond the phi-ladder.